Sparsity-Based Multipath Exploitation for Through-the-Wall Radar Imaging (eBook)

Supervisor’s Foreword 6
Supervisor’s Foreword 8
Acknowledgements 10
Contents 12
Acronyms 15
Symbols 17
1 Introduction and Motivation 21
1.1 Motivation 22
1.2 State-of-the-Art 22
1.3 Contributions 24
1.4 Thesis Overview 24
References 25
2 Fundamentals of Compressive Sensing 29
2.1 Assumptions and Conditions for Reconstruction 30
2.1.1 Sensing on Linear Bases 30
2.1.2 Sparsity 31
2.1.3 Conditions on the Measurement Matrix 32
2.2 Reconstruction Algorithms 33
2.2.1 Optimization-Based Approaches 34
2.2.2 Greedy Approaches 35
2.3 Application to Through-the-Wall Radar Imaging 36
References 37
3 Signal Model 40
3.1 Ultra-Wideband Signal Model 41
3.2 Stepped-Frequency Signal Model 43
3.3 Multipath Propagation 44
3.3.1 Direct Path and Wall Ringing Multipath 46
3.3.2 Interior Wall Multipath 47
3.3.3 Bistatic Received Signal Model 48
3.4 Direct Wall Reflections 51
3.5 Efficient Sampling Schemes 53
3.5.1 Ultra-Wideband Pulse Radar 54
3.5.2 Stepped-Frequency Radar 54
References 55
4 Sparsity-Based Multipath Exploitation 57
4.1 Motivation 57
4.2 Conventional Image Formation 58
4.3 Stationary Targets 60
4.3.1 Conventional Sparse Reconstruction 61
4.3.2 Group Sparse Reconstruction 61
4.3.3 Sparse Reconstruction with Overlapping Groups 63
4.3.4 Simulation and Experimental Results 65
4.4 Stationary and Moving Targets 68
4.4.1 Apparent Doppler Speed 68
4.4.2 Joint Target Location and Velocity Estimation 70
4.4.3 Target Location Reconstruction with Subsequent Velocity Estimation 71
4.4.4 Simulation and Experimental Results 74
4.5 Distributed Radar 82
4.5.1 Multiple Radar Unit Model 82
4.5.2 Dictionary Analysis 84
4.5.3 Joint Group Sparse Reconstruction 86
4.5.4 Simulation Results 88
4.6 Conclusions 92
References 92
5 Mitigating Wall Effects and Uncertainties 95
5.1 Motivation 95
5.2 Front Wall Reflections 97
5.2.1 Wall Reflection Model 97
5.2.2 Separate Reconstruction 99
5.2.3 Joint Group Sparse Reconstruction 99
5.2.4 Joint Overlapping Group Sparse Reconstruction 100
5.2.5 Simulation and Experimental Results 101
5.3 Wall Location Correction 105
5.3.1 Multipath Model Including Wall Position Errors 105
5.3.2 Joint Sparse Reconstruction and Wall Position Estimation 106
5.3.3 Simulation and Experimental Results 108
5.4 Conclusions 114
References 114
6 Conclusions and Outlook 116
6.1 Conclusions 116
6.1.1 Multipath Model 116
6.1.2 Sparsity-Based Multipath Exploitation 117
6.1.3 Mitigating Wall Effects and Uncertainties 117
6.2 Outlook 118
6.2.1 Signal Model 118
6.2.2 Sparsity-Based Multipath Exploitation 118
6.2.3 Sparse Reconstruction with Parameter Uncertainties 119
References 119
A 121
A.1 Complex Amplitude Derivation 121
A.2 Justification of the Invariance of Complex Amplitude Across the Array 122
Appendix Curriculum Vitae 123